YES(?,O(n^1)) 0.00/0.19 YES(?,O(n^1)) 0.00/0.19 0.00/0.19 We are left with following problem, upon which TcT provides the 0.00/0.19 certificate YES(?,O(n^1)). 0.00/0.19 0.00/0.19 Strict Trs: 0.00/0.19 { f(x, a()) -> x 0.00/0.19 , f(x, g(y)) -> f(g(x), y) } 0.00/0.19 Obligation: 0.00/0.19 runtime complexity 0.00/0.19 Answer: 0.00/0.19 YES(?,O(n^1)) 0.00/0.19 0.00/0.19 The input is overlay and right-linear. Switching to innermost 0.00/0.19 rewriting. 0.00/0.19 0.00/0.19 We are left with following problem, upon which TcT provides the 0.00/0.19 certificate YES(?,O(n^1)). 0.00/0.19 0.00/0.19 Strict Trs: 0.00/0.19 { f(x, a()) -> x 0.00/0.19 , f(x, g(y)) -> f(g(x), y) } 0.00/0.19 Obligation: 0.00/0.19 innermost runtime complexity 0.00/0.19 Answer: 0.00/0.19 YES(?,O(n^1)) 0.00/0.19 0.00/0.19 The input was oriented with the instance of 'Small Polynomial Path 0.00/0.19 Order (PS)' as induced by the safe mapping 0.00/0.19 0.00/0.19 safe(f) = {1}, safe(a) = {}, safe(g) = {1} 0.00/0.19 0.00/0.19 and precedence 0.00/0.19 0.00/0.19 empty . 0.00/0.19 0.00/0.19 Following symbols are considered recursive: 0.00/0.19 0.00/0.19 {f} 0.00/0.19 0.00/0.19 The recursion depth is 1. 0.00/0.19 0.00/0.19 For your convenience, here are the satisfied ordering constraints: 0.00/0.19 0.00/0.19 f(a(); x) > x 0.00/0.19 0.00/0.19 f(g(; y); x) > f(y; g(; x)) 0.00/0.19 0.00/0.19 0.00/0.19 Hurray, we answered YES(?,O(n^1)) 0.00/0.19 EOF